Antialiasing fractals - how best to do it?

[Timeroot]

Sadly, all three still have some "false ripples" (don't know if there's a name for them) near the center of the seahorse, which is another one of the effects that anti-aliasing is trying to avoid. Has anyone ever tried over-sampling on a hex grid, then taking all the hexagons within the square for the down sampling? Could maybe get rid of the ripples; at the same time, might introduce new ones. 

[Botond Kósa]

Sadly, all three still have some "false ripples" (don't know if there's a name for them) near the center of the seahorse, which is another one of the effects that anti-aliasing is trying to avoid.

I see, there is still some moire in the center of the image. In fact, the simple mean filtering of colors is best at removing this (but it spoils the saturation of the colors). Btw, anyone tried the color filtering in the HSL space instead of RGB? Maybe that could keep the saturation on a higher level.

Has anyone ever tried over-sampling on a hex grid, then taking all the hexagons within the square for the down sampling? Could maybe get rid of the ripples; at the same time, might introduce new ones. 

I implemented this in a previous version, but it had no visible effect on removing the moire patterns. Stochastic supersampling (Poisson disc & others) may be better suited for this.